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Keemic family
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Supermagic
|
Supernatural
These are the
planar temperament
s tempering out the keema, 875/864.
Supermagic
Comma: 875/864
7 and 9 limit minimax
[|1 0 0 0>, |0 1 0 0>, |5/4 3/4 1/4 -1/4>,
|5/4 3/4 -3/4 3/4>]
Eigenmonzos: 2, 4/3, 7/5
Lattice basis: 6/5 length=0.8879 3/2 length=1.3391
Angle(6/5, 3/2) = 77.834
Map to lattice: [<0 0 -1 3|, <0 1 1 0|]
Map: [<1 0 0 5|, <0 1 0 3|, <0 0 1 -3|]
Generators: 2, 3, 5
Edos: 7, 8, 15, 18, 19, 22, 26, 34, 37, 41, 56, 60
Projection pair
: 7 864/125
Scales:
supermagic15
11-limit
Commas: 100/99, 385/384
Map: [<1 0 0 5 2|, <0 1 0 3 -2|, <0 0 1 -3 2|]
EDOs: 7, 15, 19, 22, 37, 41, 63, 104, 145c, 201ce, 242ce, 264bce, 305bce
Badness: 0.000641
Supernatural
Commas: 225/224, 245/243
Map:[<1 0 2 -1 0|, <0 5 1 12 0|, <0 0 0 0 1|]
EDOs: 19, 22, 41, 82e, 101cd, 104, 123ce, 142cd, 224cde, 265cde
Badness: 0.000888
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These are the planar temperaments tempering out the keema, 875/864.
Supermagic
Comma: 875/8647 and 9 limit minimax
[|1 0 0 0>, |0 1 0 0>, |5/4 3/4 1/4 -1/4>,
|5/4 3/4 -3/4 3/4>]
Eigenmonzos: 2, 4/3, 7/5
Lattice basis: 6/5 length=0.8879 3/2 length=1.3391
Angle(6/5, 3/2) = 77.834
Map to lattice: [<0 0 -1 3|, <0 1 1 0|]
Map: [<1 0 0 5|, <0 1 0 3|, <0 0 1 -3|]
Generators: 2, 3, 5
Edos: 7, 8, 15, 18, 19, 22, 26, 34, 37, 41, 56, 60
Projection pair: 7 864/125
Scales: supermagic15
11-limit
Commas: 100/99, 385/384Map: [<1 0 0 5 2|, <0 1 0 3 -2|, <0 0 1 -3 2|]
EDOs: 7, 15, 19, 22, 37, 41, 63, 104, 145c, 201ce, 242ce, 264bce, 305bce
Badness: 0.000641
Supernatural
Commas: 225/224, 245/243Map:[<1 0 2 -1 0|, <0 5 1 12 0|, <0 0 0 0 1|]
EDOs: 19, 22, 41, 82e, 101cd, 104, 123ce, 142cd, 224cde, 265cde
Badness: 0.000888